Optimal decision rules for determining the length of the production run

During the production period in some industrial processes, the process mean is shifted owing to the occurrence of an assignable cause. In other situations, simultaneous changes in process mean and process variance are experienced as time passes. When the changes are time dependent, the process mean and the process variance drift steadily as time goes on, and subsequently drive the process into an out-of-control state. Thus, at any point in the, a total change in product quality may result from drift or shift or both. This paper describes how to determine the optimal production run for a process under such conditions. The process is in control at the beginning of the production run and is shut down at the end for resetting. It is assumed that the process is subject to drift and/or shift. A cost function is developed that consists of the cost of resetting the process, the cost of rejected items, the lost product cost due to shutdown and the sampling cost. Optimal production run is determined by minimizing the cost function. A search algorithm as well as a graphical method are employed to locate the optimum solution.